This invention relates to visualization of n-band multispectral/multisensor images that can be used by image analysts to better discriminate image data acquired by multispectral/multisensor systems. This invention can also be used by automated and semi-automated image understanding systems that utilize such n-band imagery. The invention can be used to aid the color blind in seeing local contrast in color images. This invention can also be used for image compression.
The advent of new remote sensing and imaging technologies provides ever increasing volumes of multispectral data. Faced with this information explosion, it has become necessary to develop methods for analysis of such high dimensional datasets. One key aspect of this process is the visualization of multispectral data, to be used for photointerpretation. This allows an image analyst to determine regions of interest and important features in the image for further analysis or segmentation. In order to take full advantage of the human visual system, a Red-Green-Blue composite image is usually generated from the data by one of a number of statistical methods such as with Principal Components Analysis. The new method here produces a one-band, grayscale visualization image from a given multispectral dataset. This is done so as to preserve as much local image contrast xe2x80x98feature informationxe2x80x99 as possible. An m-dimensional image, 1 less than m less than n, visualization for an n-dimensional image can also be obtained most optimally preserving local contrast data.
Computation of contrast, which includes computation of gradient and zero-crossings, has been used in computer vision as one of the primary methods for extracting grayscale and color features. It seems plausible, therefore, that the correct way to compare versions of the same image in terms of feature information is through their contrast content. Contrast, however, is defined a priori only for grayscale images, so it is hard to readily compare multiband images amongst themselves or multiband images with grayscale images. The first step is thus to define contrast for a multiband image. This is achieved through the introduction of a differential form on the image, computed in terms of the spectral map and a metric defined on photometric space. This reduces to the standard notion of contrast in grayscale images.
Once contrast has been defined for an arbitrary image, it is natural to ask which grayscale image most closely matches the contrast information of a given multiband image. Or, how is it possible to convert a multiband image to grayscale while preserving as much contrast information as possible?
It should be noted that the solution to this problem has multiple applications. As a data compression algorithm, it provides a n:1 image compression ratio, while preserving edge feature information. In the biomedical field, one could use this algorithm to fuse data from different sensor modalities such as CAT, PET and MRI. For the remote sensing community, this algorithm provides a visualization tool for realizing the full edge information content in hyperspectral images, such as those obtained through satellite imaging. Such high-dimensional photometric data is not easily tractable by traditional methods; in this context this new method yields a useful data analysis tool.
Perhaps the simplest possible transformation from a multispectral image to a grayscale image is averaging of the spectral bands. This produces a visualizable image which contains information from all the bands in a unified way. However, this method fails to take into account any measure of the information content in the dataset. A minor modification can be obtained by considering a weighted average, where different bands will contribute differently to the final result, depending on some pre-assigned assesment of their relative relevance in the overall image. Since it may be difficult or even impossible to determine a priori which bands should be emphasized over others, this method suffers from similar problems as unweighted averaging.
In order to overcome the shortcomings of averaging methods, statistical information about the multispectral image can be taken into account. Principal Component Analysis (PCA) achieves this by considering an n-band image as a set of vectors in an n-dimensional vector space. PCA obtains a one-band image from a multispectral image by projecting the entire distribution of spectral values onto the line spanned by the eigenspace of the covariance matrix with largest eigenvalue, and then perhaps re-scaling the result to fit the dynamic range of the output device (printer, monitor, etc). The difference then, between PCA and weighted averaging is that the line onto which projection is chosen is selected ahead of time in the latter, whereas in the former it is determined by the global statistics of the particular image at hand. However, since both methods have a common geometric foundation, they share a common problem. To see this clearly consider the following argument. It is easy to see that the cosine of the anglexcex8 between any diagonal vector in an n-dimensional vector space and any one of the coordinate axis is given by cos xcex8=1/{square root over (n)}. Hence as the dimension increases, diagonals tend to become orthogonal to the coordinate axes. Upon projecting the spectral measurements onto a fixed axis or a principal axis in photometric space, the contrast between adjacent pixels is always foreshortened, and it follows from the foregoing that this phenomenon becomes more severe as the dimensionality of the data increases.
Briefly, then, according to the present invention a method is presented for the treatment and visualization of local contrast in n-dimensional multispectral images, which directly applies to n-dimensional multisensor images as well. A 2xc3x972 matrix called the contrast form is defined comprised of the first derivatives of the n-dimenional image function with respect to the image plane, and a local metric defined on n-dimensional photometric space. The largest eigenvector of this 2xc3x972 contrast form encodes the inherent local contrast at each point on the image plane. It is shown how a scalar intensity function defined on n-dimensional photometric space is used to select a preferred orientation for this eigenvector at each image point in the n-dimensional image defining the contrast vector field for an n-dimensional image. A grey level visualization of local n-dimensional image contrast is produced by the greylevel image intensity function such that the sum of the square difference between the components of the gradient vector of this intensity function and the components of the contrast vector field is minimized across the image plane. This is achieved by solving the corresponding Euler-Lagrange equations for this variational problem. An m-dimensional image, 1 less than m less than n, visualization of n-dimensional data is produced by an m-dimensional image function such that the sum of the square difference between the components of the contrast form of this m-dimensional image and the components of the contrast form for the n-dimensional image is minimized across the image plane.